222 



THE POPULAB EDUCATOR 



LESSONS IN ARITHMETIC. XIY. 



DECIMALS (continued.). 

 . Multiplication of Decimals. 

 To multiply 6'34 by 2'149. 



6-34 x 2-149 = fg* x 



634 x 2149 



Now the numerator shows us that we must multiply the 

 figures together as in whole numbers, and the denominator 

 shows us that the result will have as many decimal places as 

 there are decimal places in the multiplier and multiplicand 

 together. 



634 x 2149 = 1362466, 



and the required result must have 5 decimal places. Hence the 

 answer is, 13"62466. 



Hence we see the truth of the 



Rule for the Multiplication of Decimals. 



Multiply the two numbers together, as in whole numbers, and 

 cut off from the resulting product as many decimal places as the 

 sum of the number of decimal places in the multiplier and 

 multiplicand. 



Ols, When the number of significant figures in the product 

 is not as great as the sum of the number of decimal places in 

 the multiplier and multiplicand, we must prefix ciphers. 



EXAMPLE.- -Multiply -013 by -02. 



Mubi.iCT-g as in whole numbers, we get 26 ; but since there 

 are 5 decimal places in the multiplier and multiplicand together, 

 we prefix 3 ciphers to 26, and the required result is by the rule 

 00026. 



The reason of this may also be seen analytically thus : 

 013 X -02 = T&b X TOO = fiSoou = '00026 (Arts. 5, 6). 

 EXERCISE 32. 



1. Find the products of the following numbers, and point 

 them according to rule : 



15. 213-02 x 4-318. 



16. 10-2016 x 38-26. 



17. 164-023 x 1-678. 



18. 9-40061 x 15-812. 



19. 7-31042 x 10-021. 



20. 40-4368 x 1-2904. 



21. 75-35060 x 62-3906. 



22. 31-50301 x 17-0352. 



23. 0-000713 x 2-30561. 



24. 42-10062 x 3-821013. 



25. 1-0142034 x -0620034. 



26. 64-301257 x 1-000402. 



1. -96 x -5 



2. '358 * -096. 



3. 1-0013 x -25. 



4. 3-6051 x 4-1. 



5. -1003 x 6-12. 



6. 8-0004 x -004. 



7. '0006 x -00012. 



8. -3005 x -0035.. 



9. 100-0008 x -000306. 



10. 25067823 x -0000001. 



11. 394-20023 x -00000003. 



12. 2564-21035 x 4 '300506. 



13. 44-046 x -43. 



14. 35-601 x 1-032. 



27. 840003-1709 x 112-10371. 



28. 0-834567834 x -00000008. 



2. In 1 rod there are 16'5 feet : how many feet are there in 

 41-3 rods ? 



3. In 1 degree of the earth's circumference there are 69'05 

 British miles : how many miles are there in 360 degrees ? 



4. In 1 barrel there are 31 - 5 gallons : how many gallons in 

 65-25 barrels ? 



5. In 1 inch there are 2 "25 nails : how many nails are there 

 in 60'5 inches ? 



6. In 1 square rod there are 30'25 square yards : how many 

 square yards are there in 26'05 rods ? 



7. In 1 square rod there are 272'25 square feet : how many 

 square feet are there in 160 rods ? 



HISTORIC SKETCHES. YIL 



KING CHARLES'S VETO ON EMIGRATION. 



FATE was almost cruel to King Charles the First. One act of 

 his, or rather let us call it one act of his government, recoiled 

 more upon his head than ever foul cannon recoiled upon its 

 gunner. Eight vessels were lying in the Thames in the early 

 part of the year 1637, bound for " the plantations" in America. 

 When they were about to sail, an order came from the king in 

 council forbidding the masters of them to go. Obedience was 

 exacted by the royal officers from the all-unwilling masters, and 

 the intending passengers were compelled to land again, to dis- 

 embark their baggage, and to renounce the object of their 

 voyage. The ships were emigrant ships, laden with colony- 

 founders' stores, and 'intended for colonists' use; the people 

 who had taken passage in them were of the stuff from which 



colonies nay, empires are made ; and the object of the people 

 in going was to establish a settlement where politics and religion, 

 which were discouraged at home, might have freedom to live, 

 and liberty to grow. An embargo wr,s laid upon the ships, and 

 for the time their departure was delayed. Some of the would-bo 

 voyagers never pursued their journey ; they refused to give the 

 guarantees which were required of them before they could get 

 licence to go ; they returned to their homes and their duty, an<2 

 made themselves names in English history for ever. Among 

 them were John Hampden, who first tried conclusions with the 

 king by refusing to pay a tax levied by the royal authority only ; 

 Sir Arthur Hazelrig, one of the most determined enemies the 

 kingly power ever had ; John Pym, the future leader of the 

 House of Commons, and promoter of all the constitutional 

 resistance which Parliament subsequently offered to the king's 

 illegal pretensions ; anil last, not least, Oliver Cromwell ! These 

 and many kindred spirits were flying from tyranny and oppres- 

 sion at home, going with their worldly wealth to follow in the 

 footsteps of the Pilgrim Fathers, who, a few years before, had 

 sailed and founded in the wild regions of the West a colony 

 where freedom was to flourish till it grew up and overshadowed! 

 the land. 



Certainly fate was cruel. Had these eight ships sailed'. 

 Had Cromwell, and Pym, and Hampden, and the rest, been 

 suffered to depart, how might not English history have been 

 written differently ? None, of course, can tell whether, among 

 the noble army of patriots who at that time thronged Parlia- 

 ment, there might not have been found another Hampden, 

 another Pym to impeach Lord Strafford, another " Cromwell, 

 guiltless of his country's blood;" but taking the men as they 

 were at the time, and considering what they afterwards became, 

 it is excusable to speculate upon what different scenes would 

 have presented themselves, had not the unlucky order of em- 

 bargo been issued from the privy council. 



But why were these men going ? England had been the 

 home, not of themselves only, but of their forefathers for gene- 

 rations. Cromwell's family counted among its recent members, 

 as poor Charles afterwards found, and tried to use the knowledge 

 in bribing his enemy that same Henry Cromwell who was 

 secretary to Cardinal Wolsey, and who, after that statesman's 

 fall in 1530, had risen in King Henry's service, till he became 

 Earl of Essex, and was finally promoted to the honour of being 

 executed, by order of the master he had served too well the 

 master " whose commands," as Mr. Hallam tersely observes, 

 " were crimes." The other emigrants were no less illustrious, 

 no less bound by the strongest ties to the land of their birth. 

 What motive could they have for voluntarily forsaking all that 

 was dear to them in nationality, and turning their backs upon 

 the country they loved ? Disgust at things as they were in the 

 country, and despair of ever seeing them become better. Shortly- 

 stated, these were the causes which drove such men away. 



" We strove for honours 'twas m vain : for freedom 'tis no more," 



they might have said with the indignant Eoman citizens. 



Henry the Eighth had begun that system of ruling by virtue 

 of his own strong will, which the nation afterwards, for national 

 purposes and under circumstances of national danger, allowed 

 his daughter Elizabeth also to exercise. But even under her, 

 beneficent and nationally glorious as her reign was, the people, 

 by their representatives in Parliament, were perpetually striving 

 to put a bridle on that sovereign power which the queen was so 

 fond of wielding. They loved her much, but they loved their 

 children more, and they would not suffer her to forge chains for 

 freeborn limbs, nor permit that they and theirs should breathe 

 by royal permission. When the dangers which caused the 

 people for a while to submit themselves wholly to her, had 

 passed away, no time was lost in winning back rights and 

 privileges which Elizabeth and her high-handed father had 

 taken into their own hands. In the re-conquest it was inevitable 

 that collisions should take place between the queen and the 

 Parliament, and collisions did actually take place ; but owing- 

 to the perseverance of the House of Commons, and to the great 

 good sense of Elizabeth, who always knew when to loosen the 

 reins which were being held too short, the result of these dis- 

 putes was always favourable to right and liberty, and never cost 

 the queen a whit of her people's affection. But when she died, 

 in 1603, and was succeeded by James of Scotland, there wero 

 still some ugly instruments at the disposal of the crown againsv 



